SOLUTION: A machine has two wheels tangent to each other. The distance between centers is 9 in. The sum of the areas is 198 sq. in. Find radius of each wheel, to the nearest hundredth of

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Question 1105369: A machine has two wheels tangent to each other. The distance between centers is 9 in. The sum of the areas is 198 sq. in. Find radius of each wheel, to the nearest hundredth of an inch.
Area of circle; pi * r^2.
radius; d/2.
Let wheels = x and y.
Not sure how to solve. Non-homework.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A machine has two wheels tangent to each other. The distance between centers is 9 in. The sum of the areas is 198 sq. in. Find radius of each wheel, to the nearest hundredth of an inch.
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x + y = 9
pi*(x^2 + y^2) = 198
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x^2 + y^2 = 198/pi
y = 9-x
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x^2 + 81-18x+x^2 = 198/pi
2x^2 - 18x + 81-198/pi = 0
2x^2 - 18x + 17.9746 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=180.202859715125 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7.85599146783708, 1.14400853216292. Here's your graph:

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x & y are the 2 solutions, they're interchangeable.
The sum of the 2 is 9.
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